Express your answer as a mixed number simplified to lowest terms. $17\dfrac{1}{6}-2\dfrac{1}{5} = {?}$
Solution: Find a common denominator for the fractions: $= {17\dfrac{5}{30}}-{2\dfrac{6}{30}}$ Convert ${17\dfrac{5}{30}}$ to ${16 + \dfrac{30}{30} + \dfrac{5}{30}}$ So the problem becomes: ${16\dfrac{35}{30}}-{2\dfrac{6}{30}}$ Separate the whole numbers from the fractional parts: $= {16} + {\dfrac{35}{30}} - {2} - {\dfrac{6}{30}}$ Bring the whole numbers together and the fractions together: $= {16} - {2} + {\dfrac{35}{30}} - {\dfrac{6}{30}}$ Subtract the whole numbers: $=14 + {\dfrac{35}{30}} - {\dfrac{6}{30}}$ Subtract the fractions: $= 14+\dfrac{29}{30}$ Combine the whole and fractional parts into a mixed number: $= 14\dfrac{29}{30}$